1. 2.5 Normal Distribution SWBAT calculate areas under a standard normal curve in writing by converting between values and z- scores using a GCD or Table Warm Up: Pg 81 Exercise 84.

2. Why Normal Distributions? It tells how variability in repeated measurements often behave It tells you how variability in populations often behave Its tells you how means computed from random sample behave

3. 2.5 The Normal Distribution The Standard Normal Distribution Normal Distribution with a mean of 0 and SD of 1 Total area under the curve = 100% Standard Normal Distributions are symmetrical Variable along the horizontal axis is the z-score To find area or z-score, can use table (pg 824-825) or calculator

4. Pg 85 D28 For the standard normal distribution: a) what is the median? b) what is the lower quartile? c) what z-score falls at the 95 th percentile? d) what is the IQR

5. 2.5 The Normal Distribution The Standard Normal Distribution

6. 2.5 The Normal Distribution Standard Units Any normal distribution can be re- centered and re-scaled to become a standard normal distribution. Formula: Calculator usage: NORMALCDF, INV NORM

7. 2.5 The Normal Distribution Solving Problems Always draw a picture!  Worth pts Shade the part of the normal curve you are trying to find If you are looking for a percentage, you need a z-score (maybe even 2!) If you are looking for another value, you will still need the z-score. Solve for the unknown.

8. 2.5 The Normal Distribution Central Intervals – See Handout 68% of the values lie with 1 SD of the mean 95% of the values lie within 2 SD of the mean 99.7% of the values lie within 3 SD of the mean 90% of the values lie within 1.645 SD of the mean

9. Pg 92 D31 Use Table A to verify that 99.7% of the values in a distribution lie within three standard deviations of the mean.

10. Problems Practice for Normal Distribution WS Pg 92 P32-39 Homework: Pg 93-94 E:59, 61, 63, 64, 67, 69, 71